Question: Solve for $p$, $ \dfrac{p - 1}{16p} = -\dfrac{6}{8p} - \dfrac{7}{8p} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $16p$ $8p$ and $8p$ The common denominator is $16p$ The denominator of the first term is already $16p$ , so we don't need to change it. To get $16p$ in the denominator of the second term, multiply it by $\frac{2}{2}$ $ -\dfrac{6}{8p} \times \dfrac{2}{2} = -\dfrac{12}{16p} $ To get $16p$ in the denominator of the third term, multiply it by $\frac{2}{2}$ $ -\dfrac{7}{8p} \times \dfrac{2}{2} = -\dfrac{14}{16p} $ This give us: $ \dfrac{p - 1}{16p} = -\dfrac{12}{16p} - \dfrac{14}{16p} $ If we multiply both sides of the equation by $16p$ , we get: $ p - 1 = -12 - 14$ $ p - 1 = -26$ $ p = -25 $